Basic Rust Removal
Surface rust can often be removed using a simple solution of one part white vinegar and one part water. Soak the piece for 30 minutes in a container large enough to treat the entire grate at once. If not completely submerged in the vinegar solution, the result will be an unevenness of color. Then scrub using a stainless steel scouring pad or steel wool, and rinse well. Additional half hour soaks/scrub sessions may be necessary and are OK, but don't leave the piece soaking for longer periods. Once free of rust, the piece should be thoroughly rinsed, dried, and seasoned to prevent the return of the rust.
Next, you go to the hand tools. I use a variety of things for the final touches before seasoning, and only items that will not mar the iron.
Items I find useful include stainless steel Chore Boy™ scrubbers (never brass or copper, they will transfer their color to the iron), and a medium stainless steel bristled brush. Popsicle sticks and expired credit/gift cards cut into shapes are great for getting into crannies to scrape and chip away at stubborn bits. Bamboo skewers work well for deep cleaning loosened crud from fine details. Use 0000 steel wool for a final once-over on smooth surfaces.
Sometimes, there are some stubborn dark stains left behind, and that's not unusual. The thinking is don't use anything harsh to try to remove them or you risk damaging metal.
Humphrey's DownEast Beast W/BBQ Guru